How can we numerically solve the below to equations using R multiroot function when E_(μ,σ) (X)=1 and 〖var〗_(μ,σ) (X)=1 ? I am interested in finding the values of μ and σ.

mean and variance of truncated normal distribution

Here α=(a-μ)/σ and β=(b-μ)/σ. I used the following code, but I’m not getting an answer. Is there any other code I may use to get what I want ?

mubar<-1
sigmabar<-1
a<-0.5
b<-5.5

model <- function(x)c(F1 = mubar-x[1]+x[2]*((pnorm((b-x[1])/x[2])-pnorm(a-x[1])/x[2])/(dnorm((b-x[1])/x[2])-dnorm((a-x[1])/x[2]))),
                       F2 = sigmabar^2-x[2]^2(1-(((b-x[1])/x[2]*pnorm((b-x[1])/x[2])-(a-x[1])/x[2]*pnorm((a-x[1])/x[2]))/(dnorm((b-x[1])/x[2])-dnorm((a-x[1])/x[2])))-((pnorm((b-x[1])/x[2])-pnorm((a-x[1])/x[2]))/(dnorm((b-x[1])/x[2])-dnorm((a-x[1])/x[2])))^2) )

(ss <- multiroot(f = model, start = c(1, 1)))